Obstructed Atomic Insulators and Superfluids of Fermions Coupled to $\mathbb{Z}_2$ Gauge Fields

TL;DR

This paper explores how fermions coupled to $ ext{Z}_2$ gauge fields on a lattice can realize obstructed atomic insulators with higher-order topology and exhibit a rich phase diagram of superfluid phases, including BCS to BEC crossover.

Contribution

It introduces a model of fermions with spatially modulated hopping coupled to $ ext{Z}_2$ gauge fields, revealing new topological insulators and superfluid phases with first-order transitions.

Findings

Realization of obstructed atomic insulators with higher-order topology.

Identification of multiple superfluid phases mediated by gauge fields.

Observation of first-order transitions from BCS to BEC superfluidity.

Abstract

We study spin-$\frac{1}{2}$ fermions coupled to $\mathbb{Z}_2$ gauge fields on a lattice. We show how a spatial modulation of the fermion hopping allows for the realization of various obstructed atomic insulators that host higher-order band topology. Studying the effect of quantum dynamics of the gauge fields within a simplified model, we find a rich phase diagram of this system with a number of superfluid phases arising from the attractive interactions meditated by the gauge fields. A key finding of this work is that the evolution from the Bardeen-Cooper-Schrieffer (BCS) superfluid state to a Bose-Einstein condensate (BEC) of tightly bound pairs occurs via the realization of these different superfluid phases separated by first-order transitions.